Given the binary tree T below.

a$)$ Insert a number on top of each node, starting from $0$ for the root, according to level numbering of potential positions of tree $\backslash ($ T $\backslash )(2$ points$)$

b$)$ For every node $\backslash ($ v $\backslash )$ of $\backslash ($ T $\backslash ),$ define an integer numbering function $\backslash ($ f$($v$)\backslash )($level numbering function$)$

$-$ If $\backslash ($ v $\backslash )$ is the root of $\backslash ($ T $\backslash ),$ then $\backslash ($ f$($v$)=\backslash )$

$-$ if $\backslash ($ v $\backslash )$ is left child of node $\backslash ($ u $\backslash )$ then $\backslash ($ f$($v$)=\backslash )$

$-$ if $\backslash ($ v $\backslash )$ is right child of node $\backslash ($ u $\backslash )$ then $\backslash ($ f$($v$)=\backslash )$

$(2$ points$)$

c$)$ Represent this binary tree T by means of an array using numbering function $\backslash ($ f$($v$)\backslash )$

$($hint: draw a single dimensional array with each cell representing the node value and label each cell with a correct array index $)(6$ points$)$